The spatial and temporal distribution characteristics of different types of thermodynamic variables and potential vorticity during precipitation were compared and analyzed in this study. On the basis of the heavy rainfall events in Jilin Province on 13–14 July 2017, the following five types of potential temperature were calculated with model outputs: conventional potential temperature (θ), equivalent potential temperature (θ_e), generalized potential temperature containing a condensation probability function (θ_Gao), generalized potential temperature containing a freezing probability function (θ_Wang), and potential temperature covering condensation and freezing (θ_Gu). The relationships between five associated types of potential vorticity [PV(θ), PV(θ_e), PV(θ_Gao), PV(θ_Wang), and PV(θ_Gu)]and precipitation were also analyzed. Results showed that the generalized potential temperature introducing a freezing probability function (θ_Wang) and its potential vorticity [PV(θ_Wang)] corresponded well with heavy rainfall. The differences between θ_Wang and θ_Gao were observed at 5–11 km in the mid-upper troposphere over the rainfall region. θ_Wang was always greater than θ_Gao, with the maximum difference reaching 2.5 K. Hence, the introduction of the freezing probability function extends the application scope of the generalized potential temperature and offers a reliable depiction of the thermodynamic state of nonuniform saturated moist air over rainfall regions. The differences among the five types of potential vorticity were mainly observed under 12 km over the rainfall region. The positive and negative anomaly centers for potential vorticity PV(θ_Gao) and PV(θ_Wang) respectively defined by θ_Gao and θ_Wang were increasingly visible. The anomaly value of PV(θ_Wang) was greater than that of PV(θ_Gao), and the differences could reach ±0.2 PVU. Such difference was due to the enhancement of the generalized potential temperature over the rainfall region resulting from the introduction of the freezing probability function. This condition led to the abnormal enhancement of the moist potential vorticity in the freezing region.